The increasing complexity of oil and gas reservoirs has led to the need of a better understanding of the processes governing the rock properties. Traditional theoretical and empirical models often fail to predict the behavior of carbonates, tight gas sands and shale gas, for example. An essential part of the necessary investigation is the study of the phenomena occurring at the pore scale. In this direction, the so-called digital rock physics is emerging as a research field that offers the possibility of imaging the rock pore space and simulating the processes therein directly. This report describes our work on developing algorithms to simulate viscous and electric flow through a three dimensional Cartesian representation of the porous space, such as those available through X-ray microtomography. We use finite differences to discretize the governing equations and also propose a new method to enforce the incompressible flow constraint under natural boundary conditions. Parallel computational codes are written targeting performance and computer memory optimization, allowing the use of bigger and more representative samples. Results are reported with an estimate of the error bars in order to help on the simulation appraisal. Tests performed using benchmark samples show good agreement with experimental/theoretical values. Example of application on digital modeling of cement growth and on multiphase fluid distribution are also provided. The final test is done on Bentheimer, Buff Berea and Idaho Brown sandstone samples with available laboratory measurements. Some limitations need to be investigated in future work. First, the computer potential fields show anomalous border effects at the open boundaries. Second, a minor problem arises with the decreased convergence rate for the velocity field due to the increased number of operations, leading to the need of a more sophisticated preconditioner. We intend to expand the algorithms to handle microporosity (e.g. carbonates) and multiphase fluid flow. / text

<p> High index contrast optical waveguides have recently attracted much attention as a promising platform for ultradense photonic integrated circuits. The vector nature and fine geometry of such waveguiding structures impose new challenges for numerical modeling. By introducing the high-order finite-difference method, highly accurate and efficient modeling techniques have been developed in this thesis for simulation and design of high index contrast waveguiding structures with compact size.</p> <p> High-order mode solving techniques are first presented for modal analyses. Their advantages in accuracy have been demonstrated for high index contrast optical waveguides and bent waveguides with small bending radius.</p> <p> Later, a class of high-order propagation algorithms, including the paraxial and wide-angle beam propagation methods, reflective operator method and bidirectional beam propagation method, have been developed for modeling longitudinally slow-varying structures, single waveguide discontinuity and piecewise z-invariant structures, respectively. All the proposed propagation algorithms have been shown to provide significant improvement in accuracy and efficiency in comparison with conventional methods, especially when simulating high index contrast structures with small feature size.</p> <p> Accurate modeling of evanescent waves is critical for the simulation of strongly reflecting structures with high longitudinal index contrast. Various rational approximations to square root operators used in the bidirectional beam propagation method have been comprehensively assessed. Useful guidelines for accurate modeling of evanescent and propagating modes are provided.</p> <p> Finally, the efficient high-order bidirectional beam propagation method is introduced for the design of Bragg gratings on high index contrast and plasmonic waveguides. Good performance is achieved.</p> / Thesis / Doctor of Philosophy (PhD)

Subduction zones are regions of intense earthquake activity up to great depth. Sources are located inside the subducting lithosphere and, as a consequence, seismic radiation from subduction zone earthquakes is strongly affected by the interior slab structure. The wave field of these intraslab events observed in the forearc region is profoundly influenced by a seismically slow layer atop the slab surface. This several kilometer thick low-velocity channel (wave guide) causes the entrapment of seismic energy producing strong guided wave phases that appear in P onsets in certain regions of the forearc. Observations at the Chile-Peru subduction zone presented here, as well as observations at several other circum-pacific subduction zones show such signals. Guided wave analysis contributes details of immense value regarding the processes near the slab surface, such as layering of subducted lithosphere, source locations of intraslab seismicity and most of all, range and manner of mineralogical phase transitions. <br><br> Seismological data stem from intermediate depth events (depth range 70 km - 300 km) recorded in northern Chile near 21 Grad S during the collaborative research initiative " Deformation Processes in the Andes" (SFB 267). A subset of stations - all located within a slab-parallel transect close to 69 Grad W - show low-frequency first arrivals (2 Hz), sometimes followed by a second high-frequency phase. <br><br> We employ 2-dimensional finite-difference simulations of complete P-SV wave propagation to explore the parameter space of subduction zone wave guides and explain the observations. Key processes underlying the guided wave propagation are studied: Two distinct mechanisms of decoupling of trapped energy from the wave guide are analyzed - a prerequisite to observe the phases at stations located at large distances from the wave guide (up to 100 km). Variations of guided wave effects perpendicular to the strike of the subduction zone are investigated, such as the influence of phases traveling in the fast slab. Further, the merits and limits of guided wave analysis are assessed. Frequency spectra of the guided wave onsets prove to be a robust quantity that captures guided wave characteristics at subduction zones including higher mode excitation. They facilitate the inference of wave guide structure and source positioning: The peak frequency of the guided wave fundamental mode is associated with a certain combination of layer width and velocity contrast. The excitation strength of the guided wave fundamental mode and higher modes is associated with source position and orientation relative to the low-velocity layer. <br><br> The guided wave signals at the Chile-Peru subduction zone are caused by energy that leaks from the subduction zone wave guide. On the one hand, the bend shape of the slab allows for leakage at a depth of 100 km. On the other, equalization of velocities between the wave guide and the host rocks causes further energy leakage at the contact zone between continental and oceanic crust (70 km depth). Guided waves bearing information on deep slab structure can therefore be recorded at specific regions in the forearc. These regions are determined based on slab geometry, and their locations coincide with the observations. <br><br> A number of strong constraints on the structure of the Chile-Peru slab are inferred: The deep wave guide for intraslab events is formed by a layer of 2 km average width that remains seismically slow (7 percent velocity reduction compared to surrounding mantle). This low-velocity layer at the top of the Chile-Peru slab is imaged from a depth of 100 km down to at least 160 km. Intermediate depth events causing the observed phases are located inside the layer or directly beneath it in the slab mantle. The layer is interpreted as partially eclogized lower oceanic crust persisting to depth beyond the volcanic arc. / Subduktionszonen sind bis in große Tiefen von intensiver Erdbebentätigkeit geprägt. Die Erdbebenquellen befinden sich in der subduzierten Lithosphäre (Slab), ihr Wellenfeld wird deshalb stark von der internen Slab-Struktur beeinflusst. Eine Schicht mit reduzierter seismischer Geschwindigkeit im oberen Bereich der Platte kann als Wellenleiter für diese Signale fungieren. In der nur wenige Kilometer dicken Schicht entstehen sogenannte geführte Wellen, die in Teilen des Forearc beobachtet werden. Diese Phasen bergen wertvolle Informationen über die Struktur nahe der Slab-Oberfläche, wie zum Beispiel Dicke der Schichtung, Herdlokationen und vor allem Tiefe und Art mineralogischer Umsetzungen. <br><br> Die Beobachtungen stammen von mitteltiefen Beben (70 km - 300 km) im Untersuchungsgebiet in Nord-Chile und wurden im Rahmen des Sonderforschungsbereich 267 " Deformationsprozesse in den Anden" aufgezeichnet. Stationen in einem Streifen um 69 Grad W, der sich parallel zum Streichen der Subduktionszone erstreckt, zeigen niederfrequente Ersteinsätze, denen teilweise höherfrequente Phasen folgen. <br><br> Mit Hilfe eines 2-dimensionalen Finite-Differenzen-Algorithmus werden die P-SV Wellenausbreitung simuliert, und die Beobachtungen erklärt. Zentrale Fragestellungen zu Wellenleitern in Subduktionszonen werden untersucht: Es werden zwei Mechanismen, die das Auskoppeln seismischer Energie aus dem Wellenleiter ermöglichen beschrieben - eine Grundvoraussetzung für das Auftreten von geführten Wellen in großen Entfernungen vom Wellenleiter (bis zu 100 km). Des weiteren werden Stärken und Grenzen der Analyse von geführten Wellen erörtert. <br><br> Die Spektren der geführten Wellenzüge erweisen sich als robuste Messgröße, um die Charakteristika des Wellenleiters zu bestimmt. Struktur des Wellenleiters und Quellpositionen können so für festgelegte Quell-Empfänger-Geometrien abgeleitet werden. Die Peak-Frequenz der Grundmode wird durch eine Kombination aus Dicke der Schicht und Geschwindigkeitskontrast bestimmt. Die Stärke der Anregung der Grundmode und höherer Moden lässt auf die Lage und Orientierung der Erdbebenquelle relativ zur Schicht schließen. Geschwindigkeitskontrast, Schichtdicke und Quellposition sind von herausragender Bedeutung, um mineralogische Interpretationen des Wellenleiters zu überprüfen. <br><br> Aufbauend auf die Simulationen werden die Beobachtungen interpretiert und Auskunft über die Struktur der Chile-Peru Subduktionszone erhalten: Eine dünne Schicht an der Slab-Oberfläche (durchschnittlich 2 km dick) trägt geringere seismische Geschwindigkeiten als der umgebende Mantel und fungiert als Wellenleiter für intra-platten Ereignisse in Tiefen von 100 bis mindestens 160 km. Ereignisse, die geführte Wellen hervorrufen, liegen in dieser Schicht oder direkt darunter im subduzierten Mantel. Um zu den Stationen in der Forearc-Region zu gelangen, entkoppelt ein Teil der geführten Wellen in einer Tiefe von circa 100 km aus der Niedergeschwindigkeitsschicht. Die Krümmung des Slab erlaubt das Austreten der Wellen und nimmt auch Einfluss auf die Pulsformen. <br><br> Der Wellenleiter in der Chile-Peru Subduktionszone ergibt sich als unregelmäßige Schicht mit reduzierter seismischer Geschwindigkeit, in der geführte Wellen entstehen, in unterschiedlichen Tiefen wieder austreten, und an die freie Oberfläche gelangen. Die Beobachtungsgebiete befinden sich im Forearc und werden durch die Geometrie und Struktur der subduzierten Platte festgelegt. <br><br> Die nur wenige Kilometer dicke, seismisch langsame Schicht an der Oberfläche des Chile-Peru Slab legt nahe, dass die Unterkruste der subduzierten Platte bis in große Tiefen besteht und nicht vollständig eklogitisiert ist. Abgeleitete Schichtdicke, Geschwindigkeitskontrast

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